It should be noted that, when generalizing the classical expression of the function \(\mathfrak {A}_{-}\)  defined in Eq.(REF ) to its corresponding quantum mechanics operator,
there exists ambiguities. In fact, classically \(\mathfrak {A}_{-}\)  only coincides with \(\Omega ^2_{Q}\)  in the expanding phase. The latter is a function of the phase space variables which is explicitly given by [1]}, [2]}, [3]}, [4]},
\(\Omega ^2_{Q}=3\kappa \frac{p^2_\phi }{a^4}-18\frac{p^4_\phi }{a^6\pi ^2_a}-12a\frac{p_\phi }{\pi _a}V_{,\phi }+a^2V_{,\phi \phi },\) 
